Rational solutions to the KPI equation and multi rogue waves

We construct here rational solutions to the Kadomtsev–Petviashvili equation (KPI) as a quotient of two polynomials in xx, yy and tt depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2N(N+1)2N(N+1) in xx, yy and tt depending on 2N−22N−2 real parameters for each positive integer NN. We give explicit expressions of the solutions in the simplest cases N=1N=1 and N=2N=2 and we study the patterns of their modulus in the (x,y)(x,y) plane for different values of time tt and parameters.